The distinction is a question of culpability, not just the harm caused.
The law, at least in the criminal law context, is not fundamentally consequentialist in its philosophy. The end consequence of an act for which someone is at fault in some way isn't the only thing that matters in criminal law. Instead, there is basically a two dimensional grid.
On one axis is the seriousness of the harm caused on the "eye for an eye" theory of proportionality between punishment and the harm caused. Thus, homicide is more serious than causing serious bodily injury or raping someone, which is more serious than causing bodily injury that is not serious or sexual in nature. Grand theft is more serious than shoplifting. It doesn't make economic sense to spend $70,000 a year to incarcerate someone for many years to prevent people from stealing $15 items, unless very extreme aspects of the person's criminal history suggest that this seemingly minor incident demonstrates a high risk of future offenses that are far more serious because it proves that a hardened criminal hasn't reformed himself or herself.
On the other axis is basically a measure of how evil and malicious someone would have to be to do such a thing which is called culpability.
At once extreme, first degree murder, for example, is calculated, premeditated harm to another. At the other extremes are completely non-culpable conduct (either due to lack of any fault-worthy conduct or because someone is mentally incapable in the eyes of society of engaging in culpable conduct like a baby or someone with dementia or someone having hallucinations relevant to the conduct that kills someone, ordinarily negligent conduct that kills someone, and criminally negligent conduct that kills someone. In between the extremes is conduct that is reckless or is impulsive or carried out in the heat of passion or by someone with diminished capacity.
Only moderately culpable conduct is punishable only by a civil lawsuit for compensatory damages, and non-culpable conduct isn't even punishable in a civil lawsuit in the absence of special circumstances in which strict liability is imposed in lieu of proof of culpability. Less culpable conduct commands less serious sentences, and more culpable conduct commands more serious sentences.
Why single out culpability?
Basically, this is a crude way a predicting, based upon someone's past actions, the risk that the pose in the future. (Our evaluation of culpability is further refined and adjusted by factors related to the individual defendant and not the particular offense involved, like a criminal defendant's status as a juvenile or adult, and the individuals history of prior criminal convictions.)
Conduct that constitutes first degree murder corresponds more or less to psychopathy, an incurable psychiatric condition in which someone lacks all empathy and takes selfish delight in harming others out of boredom or for personal gain. Psychopathy is a technical term that is modern abnormal psychology's closest synonym to saying that someone is unredeemable and evil, and conduct for which the death penalty is available, mostly in conduct that is most highly diagnostic of psychopathy, since the usual goal of incarceration, to return someone to the community once they are no longer an appreciably elevated threat to it, can never be achieved in the case of someone who is unredeemable and evil, because their condition is an incurable part of who they are as a person and their lack of empathy makes them incapable of emotionally distinguishing between right and wrong or feeling guilt. This intuition bears out. The more culpable an offense is, the more likely it is that the offender scores high on standardized measures of the extent to which someone displays signs of psychopathy that are exemplified in serial killers and the worst con men.
Intermediate levels of liability correspond more or less to impulsivity that can turn violent (which is associated with a variety of incurable psychiatric conditions and also with the developmental states of adolescence and young adulthood and with instances of excessive intoxicant consumption, especially in men), in which someone knows what they are doing is wrong but lacks sufficient self-control to prevent themselves from acting until it is too late and they have calmed down, at least until they "age out" or or take steps to treat the symptoms of the conditions or addictions or intoxicated excesses. Their lack of self-control makes them a potential risk to others even though they empathize and feel guilt, but not like the risk associated with a psychopath who just doesn't care at all if they are doing something that violates intuitive moral codes of conduct.
Negligence, i.e. inattentiveness and carelessness pose even less of a threat to the community and while it could be due to something like attention deficit disorder, could also be due to extenuating circumstances like sleep deprivation or being overwhelmed with too much at once to keep track of everything at once. Negligence harm generally isn't even momentarily malicious due to loss of control and the person who harms someone negligently will often immediately regret the harm that they caused and will try to refrain from doing so again and will try to make things right. Such a person is far less of a future threat to society, but still more of a threat than someone who doesn't harm others in the first place in any manner in which they are at fault.
Reasonable people (and even reasonable judges) can and do have differences of opinion on the relative importance of seriousness of harm and culpability in determining a sentence for a conviction of a particular course of illegal conduct.
The difficulty in balancing the apples and oranges factors of seriousness of harm (which, in part, reflects a person's capacity to inflict serious harm in the future and also reflects society's judgment about how serious it is to do something with ill intent) and culpability.
To insure that these factors are balanced in a predictable and fair way, we embody the weighing of those two factors in a collective legislative judgment codified in a state or national penal code, rather than a case by case decision making process by judges.
The modern trend towards giving more weight to culpability.
If anything, the tendency at the present is for legislative judgment to give more weight to culpability than it has in the past as social science methods in criminology have demonstrated that culpability demonstrated in criminal conduct actually carried out by a person is indeed highly predictive of that person's future dangerousness to society
For example, cruelty to animals is an offense which reflects very high levels of culpability despite often involving relatively modest amounts of harm viewed in a human-centric way. But, cruelty to animals is increasingly being upgraded from a misdemeanor to a felony, because it is a very diagnostic litmus test for psychopathy in an individual and very frequently eventually escalates to causing serious harm to humans.
Similarly, drunk driving when it is charged based upon a traffic stop, rather than an accident that occurred while someone was driving drunk, is a very low harm offense, just like any other traffic offense, and historically has only been a misdemeanor. But, in cases where someone is repeatedly convicted of drunk driving, the culpability is high and the conduct tends to reflect a very difficult to self-regulate addiction and substance abuse problem that is highly likely to recur and to eventually result in a high harm accident. Repeated convictions are what distinguish an incident where someone is basically just criminally negligent in driving when they should have known that they shouldn't, from the far more serious case where someone recklessly and with indifference to the well being of others drives drunk knowing full what the risk that they are exposing other people to. And because repeat drunk driving convictions are more culpable and reflect a personal character of the offender that shows a high likelihood of causing future harm to others, many states are starting to upgrade repeat drunk driving from a misdemeanor to a felony even though the actual harm from the specific incident of drunk driving that only gives rise to a traffic stop is still just as low the fifth or sixth time someone is convicted as it was the first time.
So, in sum, assigning different penalties to different levels of culpability is a way to allocate limited correctional and punishment resources in a manner proportionate to the future risk of dangerousness that the current conviction provides undeniable evidence of in a non-arbitrary manner.
Indeed, most people simply internalize the notion that more culpable conduct deserves more serious punishment because it is wrong, without conceptualizing in the more theoretical abnormal psychology informed and utilitarian framework in which I have described it above to demonstrate the implicit logic and wisdom behind the gut instinct that more culpable conduct should be punished more seriously, especially when its cause is not a passing incident that is unlikely to recur.